The Oseen-Burgers vortex is a rare exact solution to the full Navier-Stokes equations. An axial strain rate a continually pulls fluid toward the vortex core while viscosity ν diffuses vorticity outward — these balance to produce a steady vortex of core radius r_c = √(2ν/a). The azimuthal velocity is v_θ = Γ/(2πr) · (1 − e^(−ar²/2ν)), matching a potential vortex far from the axis but vanishing at the center. This solution is fundamental to turbulence: it models the coherent vortex tubes responsible for intermittent dissipation spikes observed in high-Reynolds-number flows.